Basic AC Reactive Components CAPACITANCE CAPACITANCE There are many natural causes of capacitance in AC power circuits, such as transmission lines, fluorescent lighting, and computer monitors. Normally, these are counteracted by the inductors previously discussed. However, where capacitors greatly outnumber inductive devices, we must calculate the amount of capacitance to add or subtract from an AC circuit by artificial means. EO 1.5 DEFINE capacitive reactance (XC). EO 1.6 Given the operating frequency (f) and the value of capacitance (C), CALCULATE the capacitive reactance (XC) of a simple AC circuit. EO 1.7 DESCRIBE the effect on phase relationship between current (I) and voltage (E) in a capacitive circuit. EO 1.8 DRAW a simple phasor diagram representing AC current (I) and voltage (E) in a capacitive circuit. Capacitors The variation of an alternating voltage applied to a capacitor, the charge on the capacitor, and the current flowing through the capacitor are represented by Figure 3. The current flow in a circuit containing capacitance depends on the rate at which the voltage changes. The current flow in Figure 3 is greatest at points a, c, and e. At these points, the voltage is changing at its maximum rate (i.e., passing through zero). Between points a and b, the voltage and charge are increasing, and the current flow is into the capacitor, but decreasing in value. At point b, the capacitor is fully charged, and the current is zero. From points b to c, the voltage and charge are decreasing as the capacitor discharges, and its current flows in a direction opposite to the voltage. From points c to d, the capacitor begins to charge in the opposite direction, and the voltage and current are again in the same direction. Rev. 0 Page 5 Figure 3 Voltage, Charge, and Current in a Capacitor ES-08 CAPACITANCE Basic AC Reactive Components At point d, the capacitor is fully charged, and the current flow is again zero. From points d to e, the capacitor discharges, and the flow of current is opposite to the voltage. Figure 3 shows the current leading the applied voltage by 90°. In any purely capacitive circuit, current leads applied voltage by 90°. Capacitive Reactance Capacitive reactance is the opposition by a capacitor or a capacitive circuit to the flow of current. The current flowing in a capacitive circuit is directly proportional to the capacitance and to the rate at which the applied voltage is changing. The rate at which the applied voltage is changing is determined by the frequency of the supply; therefore, if the frequency of the capacitance of a given circuit is increased, the current flow will increase. It can also be said that if the frequency or capacitance is increased, the opposition to current flow decreases; therefore, capacitive reactance, which is the opposition to current flow, is inversely proportional to frequency and capacitance. Capacitive reactance XC, is measured in ohms, as is inductive reactance. Equation (8-3) is a mathematical representation for capacitive reactance. XC 1 2πf C f = π = C = frequency (Hz) ~3.14 capacitance (farads) (8-3) where Equation (8-4) is the mathematical representation of capacitive reactance when capacitance is expressed in microfarads (µF). XC 1,000,000 2πf C (8-4) Equation (8-5) is the mathematical representation for the current that flows in a circuit with only capacitive reactance. I ES-08 E XC (8-5) Page 6 Rev. 0 Basic AC Reactive Components CAPACITANCE where I = effective current (A) E = effective voltage across the capacitive reactance (V) XC = capacitive reactance (Ω) Example: A 10µF capacitor is connected to a 120V, 60Hz power source (see Figure 4). Find the capacitive reactance and the current flowing in the circuit. Draw the phasor diagram. Figure 4 Circuit and Phasor Diagram Solution: 1. Capacitive reactance XC 1,000,000 2πf C 1,000,000 (2)(3.14)(60)(10) 1,000,000 3768 XC Rev. 0 265.4 Ω Page 7 ES-08 CAPACITANCE 2. Basic AC Reactive Components Current flowing in the circuit I E XC 120 265.4 I 3. 0.452 amps Phasor diagram showing current leading voltage by 90° is drawn in Figure 4b. Summary Capacitive reactance is summarized below. Capacitive Reactance Summary Opposition to the flow of alternating current caused by capacitance is called capacitive reactance (XC). The formula for calculating XC is: XC 1 2πf C Current (I) leads applied voltage by 90o in a purely capacitive circuit. The phasor diagram shows the applied voltage (E) vector leading (below) the current (I) vector by the amount of the phase angle differential due to the relationship between voltage and current in a capacitive circuit. ES-08 Page 8 Rev. 0